A256076 Non-palindromic balanced primes.

1823, 1933, 2141, 2251, 2633, 2963, 3061, 3391, 4091, 4253, 4363, 4583, 5393, 5717, 5827, 6637, 6857, 6967, 7829, 8147, 8419, 8969, 9067, 9397, 14303, 14503, 15013, 15313, 15413, 15913, 16223, 16823, 17033, 17333, 18043, 18143, 18443, 18743, 19553, 19753, 19853

Offset: 1

Author

Eric Angelini and M. F. Hasler, Mar 14 2015

Keywords

• nonn
• base

Comments

Here a number is called balanced if the sum of digits weighted by their arithmetic distance from the "center" is zero. Palindromic primes (A002385) are "trivially" balanced, so they are excluded here.

These are the primes in A256075, see there for further information.

See A256081 for the binary version and A256090 for the hexadecimal version.

Examples

			a(1)=1823 is balanced because 1*3/2 + 8*1/2 = 2*1/2 + 3*3/2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A256075, A256081, A256090, A002385.

Programs

Maple

filter:= proc(n) local L,m;
  L:= convert(n,base,10);
  m:= (1+nops(L))/2;
add(L[i]*(i-m),i=1..nops(L))=0  and isprime(n) and L <> ListTools:-Reverse(L)
end proc:
select(filter, [seq(i,i=1001..20000,2)]); # Robert Israel, May 29 2018

PARI

is(n,d=digits(n),o=(#d+1)/2)=!(vector(#d,i,i-o)*d~)&&d!=Vecrev(d)&&isprime(n)